AT SHINTOMI nursing home in Tokyo, men and women sit in a circle following exercise instructions before singing along to a famous children’s song, “Yuyake Koyake” (“The Glowing Sunset”). They shout out and clap enthusiastically even though the activities are being led, not by a human fitness guru, but by Pepper, a big-eyed humanoid robot made by SoftBank, a telecoms and internet giant.

Japan leads the world in advanced robotics. Many of its firms see great potential in “carerobos” that look after the elderly. Over a quarter of the population is over 65, the highest proportion of any country in the OECD. Care workers are in desperately short supply, and many Japanese have a cultural affinity with robots.

For now the market is small. Although the government expects it will more than triple between 2015 and 2020, to ¥54.3bn ($480m), that is a long way below the revenues from industrial and service robots. One big reason for that is expense; few individuals can afford their own robots. Private firms partly rely on...